Official Explanation
The least possible value for the mean of the numbers of hours of exercise reported for the week is.
Explanation
The least possible mean corresponds to the case where each individual reported the minimum amount of time for their category (i.e., 5 people exercised 0 hours, 3 people exercised 1 hour, and so on). The mean in this case would be
\(\frac{5(0)+3(1)+2(2)+4(3)+4(4)+5(5)+1(8)+1(10)}{5+3+2+4+4+5+1+1}=\frac{78}{25}=3.12\)
The correct answer is 3.12.
The number of respondents who exercised on average less than one-half hour per day during the week is between________, inclusive.
Explanation
A respondent who averaged less than one-half hour of exercise per day would have reported less than 3.5 hours of exercise for the week. There were 10 respondents who reported exercising less than 3 hours per week: those respondents necessarily averaged less than one-half hour of exercise per day. There were 11 respondents who reported exercising more than 4 hours for the week: those respondents necessarily averaged more than one-half hour of exercise per day. There were 4 respondents who reported exercising at least 3 hours but no more than 4 hours for the week. It is possible that all 4 of these respondents reported more than 3.5 hours of exercise, in which case only 10 respondents would have averaged less than one-half hour of exercise per day. It is also possible, however, that 1 or more of these 4 respondents reported fewer than 3.5 hours, in which case, up to 14 respondents would have averaged less than one-half hour of exercise per day.
The correct answer is 10 and 14.